Question

If \[36\] workers can build a wall in \[12\] days, how many days will \[16\] workers take to build the same wall? (Assuming the number of working hours per day is constant)

Answer 1

Hint: First calculate the days required for \[1\] worker to do the work then calculate the days that are required by \[16\] workers just by unitary methods. Since \[12\] days are required for \[36\] workers to do the job so to calculate the days required for \[1\] workers multiply \[36\] by total days required by these workers. Now to calculate the days required for \[16\] workers divide the total days required for \[1\] workers to build the wall by \[16\]. Hence you will get your required answer.

Complete Step by Step Solution:
Given that,
Days required by \[36\] workers to build the wall \[=12{ }days\]
Days required by \[16\] workers to build the wall \[=?\]
Since \[36\] workers take \[12\] days
So, the days required for \[1\] worker to build the same wall
\[\Rightarrow 12\times 36\] days
\[\Rightarrow 432\] days
Now we have to calculate the number of days required for \[16\] workers to build the same wall
Since \[1\] worker required to build \[=432\] days
So,
\[16\] workers require \[=432/16\] days
\[=\dfrac{432}{16}\] days
\[\Rightarrow 27\] days

Hence the days required for \[16\] workers to build the same will be \[27\].

Note:
In this type of work done questions note that the number of days to finish a work is inversely proportional to number of workers who do the work. In this we use simple unitary method that first calculates the days required to do the work for \[1\] worker then using this apply unitary method and divide this by workers whose we need to calculate the days to complete that work.